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The answer is (42,6).

Equation of a circle

29999999^2 = 899999940000001

Sum of digits = 9*6+8+4+1 = 67

from the set 1,2,3,4,5 Doug will choose three distinct numbers and Regina will choose three distinct numbers. What is the probability that Doug and Regina will choose exactly two of the same numbers as each other? Express answer as a common fraction.

Let Doug choose his three first.

How many ways can Regina pick hers up.   5*4*3=60

How many ways can Regina pick the first 2 the same and the 3rd diff from Doug     3*2*2=8

But the different one can be picked up 1st 2nd or 3rd   so that is 8*3=24

So i think the prob is  24/60   =  2/5

Or sometimes you might see it with some LaTex coding here that has not been rendered. (not used properly)

So it looks really wierd and really does not mean anything.

Thanks guest.

If you mean 

\(x+\frac{1}{x}=1\qquad then\\ x^2+1=x\\ x^2-x+1=0\\ x=\frac{1\pm\sqrt{1-4}}{2}\\ x=\frac{1\pm\sqrt{-3}}{2}\\ x=\frac{1\pm\sqrt{3}\;i}{2}\\\)

This is not a real number. So if you are only looking for real numbers then guest is right. There are no solution.

I would be considering the connectors and rods seperately and then add them together

connectors

row 0           1

row 1           2

row 2            3

etc

and add them up

rods

row 1        2

row 2        4

there will be 2 rods off each connector so row 3 will have 2*3=6 connectors

etc

 then add them up.

If you have done arithmetic progression you can add these with formula but there are not many so you can just add them all up in you head or on paper.

That is a more than ample hint  :)

Center of a circle

The way you have classified them under "rational" and "irrational" is CORRECT.

thank you!

See the second answer here: https://web2.0calc.com/questions/this-one-is-pretty-confusing-p-not-urgent-btw

we can give the width and length variables. lets call them x and y respectively. we know that y=2x-4

the perimeter is equal to 2x + 2y or 2(x + y). 

the perimeter in terms of x is 2(x + 2x-4) = 2(3x-4) = 6x-8

6x-8=46

6x=54

x=9cm

if y=2x-4, then y=9*2 - 4=18-4=14.

y=14cm

the width is 9cm and the length is 14cm

It is used in sets 

like

Set A={1,2,3,...} 

*Includes* *Ends* 

For example

{a,b,c}

{a,b,c} means the set consisting of a, b, and c.

sum of 3 consecutive integers, 

so the first integer is x

second integer is x+1 (Because it is consecutive) then the third is x+2

The sum of them is equal to 15

so

x+x+1+x+2=15

combine like terms

3x+3=15

subtract 3

3x=12

divide by 3

x=4

Find each integer just by subsituiting x=4 

first integer is x so it is = 4

second integer is x+1 so it is 5

third integer is x+2 so it is 6

Their product, 4*5*6=120 

No solution 

as

x+1/x=1 

x+1=x 

x=x-1 No real solutions 

Use mathway.com/algebra if you want to check. 

well

3^2+4^2 does equal 5^2

So if x =2 it does work

I expect there are other answers too.

This looks more useful 

(1 3 3 1 4 4 1 2 1 5 7 )3

1+3+4+1+1+7  = 17 

3+1+4+2+5     = 15

17-15=2

So when  13314412157 is divided by 11 the remainder is 2

and

when     (13314412157)^3  is divided by 11 the remainder is 2^3 = 8

I don't offhand see how this helps.

\( \frac{1^2}{10 }=\frac{1}{10}\\~\\ but\\~\\ \left(\frac{1}{10}\right)^2=\frac{1^2}{10^2}=\frac{1}{100}\)

4(3x^2 y^4)^3/(2x^3y^5)^4

\(\frac{4(3x^2 y^4)^3}{(2x^3y^5)^4}\\~\\ \)

\(4*(3x^3y^4)^3\\ =4*(3*x^3*y^4)^3\\ =4*3^3*(x^3)^3*(y^4)^3\\ =4*27*x^{3*3}*y^{4*3}\\ =4*27*x^{9}*y^{12}\\\)

Now I have done what is necessary to simplify the top.

Now it is your turn to simplify the bottom.

After that you can put it back to one problem and  cancel.

Maybe study the standard general circle equation.

Then look at the equation in the problem. 

Please attempt it!

Just an explanation of guest's answer

You have four digits

_   _   _   _
 

The first digit has 9 choices, because it can't be 0. So 1 through 9 will be 9 choices.

The second will also be 9 choices. This is because it now can include 0 but also excludes the previous digit.

The third digit has 8 choices, because it excludes the previous 2 digits.

The fourth digit has 7 choices, because it excludes the previous 3 digits.

So 9 * 9 * 8 * 7 = 4536

you got that right!
 

whenever something is square, it is MULTIPLIED by itself

so something like 1/2 squared, is also 1/2 * 1/2

so 1/10 squared is 1/10 times 1/10, which equals 1/100